i let my son have his binky for far too long, you dont want to know (4!!!) (he had GERD, and it soothed him when nothing else would, and then when i was getting ready to take it away, his dad left us and there was a long time of change so i let him keep it for security) any how what i did was have a "bye bye binky" party where we gathered up ALL of his binkies, wrapped them up like a present. (make sure to let ur child have a significant park of this), and invited some of our friends who had kids over and had a party. We had balloons and streamers in our house, and i had made a cake, and had a friend that was going to have a baby come over and my son presented her with his binkies as a gift for the new baby. (im quite sure she threw them away when she got home lol). later we had the cake and sang "no more binkies for you, no more binkies for you, no more binkies for (child's name), no more binkies for you" to the birthday melody. then he got to blow out the 1 candle.
When you do get rid of them, make sure to get ALL of the binkies, EVERY SINGLE ONE OF THEM. My son asked for a binky for about 1 week after that (not the first day though) and i said we didnt have anymore, that he gave them to so and so for the new baby. He cried for a while, or talked/sang himself to sleep (so late sometimes that if i had a binky, i would have given in because i wanted to sleep so bad!), but it wasnt very long before he stopped asking completely. oh, and while he was asking for them, i avoided going into the part of the store where they were on the shelves. since your daughter is turning 2, this would probably work really well right after her birthday, because she would associate the fun of her birthday with this party too. (also you can reuse the decorations from her paryt! and you dont have to have a store bought cake, you can have ur daughter help you make one and let her help decorate it!)
what ever you chose to do, good luck :)
I really like the idea of the build a bear thing, but at the time, it would have cost too much for me.
oh, and dont listen to people who tell you that your child is too old for a binky. that is YOUR decision, not theirs and unless you ask them for their opinion of an appropriate age to get rid of it, they can stick their opinion, and their advice where the sun doesn't shine.